I’ve read every book J.K. Rowling has published, some of them several times over. OK, all of them several times over. And still, I doubt I would have picked up on anything that would have made me think that SHE was the author behind “The Cuckoo’s Calling.”

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I almost wish I hadn’t known, so I wouldn’t have read it with some of my attention in search of clues that would have made me suspicious that the book’s author wasn’t, in fact, an ex-military police officer and was actually one of the world’s most famous storytellers.

Because this is a good story, one that is entertaining enough to merit a read even if Robert Galbraith, Rowling’s pseudonym, had been a real person who really wrote it.

“The Cuckoo’s Calling” introduces readers to Cormoran Strike, a London private detective with his own complicated backstory — he’s the son of a rock star and a groupie, has a prosthetic leg to replace the one he lost in Afghanistan during his military service, and he just ended a difficult romantic relationship. He’s also quite clever.

Along with his started-out-temporary-but-who-didn’t-know-that-was-going-to-last secretary Robin Ellacott, he looks into the death of a supermodel, Lula. Everyone assumes it was suicide, but Strike is asked to investigate it by someone who tells him it had to have been otherwise. His investigation takes Strike into the worlds of high fashion and big money as he makes his way to the truth.

Rowling’s (er, Galbraith’s? Whoever.) literary gift is on display in this work. She crafts an entertaining story with characters who hold the reader’s interest, and comes up with an ending that I’ll admit I was surprised by.

It gets a little too clever in some places, with the final denouement tying together some earlier elements in a way that’s almost a little too pat, and some of the leaps Strike makes seem a little too out-of-nowhere. And it wouldn’t be a J.K. Rowling book if it didn’t have lots and lots of description, not all of which seems necessary.

But overall, it’s a fun read, with a main character you can care about and one you’ll want to see again in other adventures. It reads like Rowling had fun writing it. There’s a certain lightness to it that was missing from her other grown-up fiction endeavor, “The Casual Vacancy.” Perhaps that came from the freedom of writing and publishing under a pseudonym without all the pressure of her own backstory. It will be interesting to see if she can maintain that sense of fun now that everyone knows it’s her and that particular mystery has been solved.